balls-up vs mistake

balls-up and mistake both are nouns.

Word	Noun	Adjective	Verb	Adverb
balls-up	Yes	No	No	No
mistake	Yes	No	Yes	No

As nouns, mistake is a hypernym of balls-up; that is, mistake is a word with a broader meaning than balls-up:

balls-up: something badly botched or muddled
mistake: a wrong action attributable to bad judgment or ignorance or inattention

Other hypernyms of balls-up include error, fault.

balls-up (noun)	mistake (noun)
something badly botched or muddled	a wrong action attributable to bad judgment or ignorance or inattention
	an understanding of something that is not correct
	part of a statement that is not correct

balls-up (verb)	mistake (verb)
	to make a mistake or be incorrect
	identify incorrectly